1. Field of the Invention
This invention relates broadly to methods for investigating subsurface earth formations. More particularly, this invention relates to methods of determining the permeability of an earth formation utilizing information obtained from a nuclear magnetic resonance (NMR) tool.
2. State of the Art
The determination of permeability and other hydraulic properties of formations surrounding boreholes is very useful in gauging the producibility of formations, and in obtaining an overall understanding of the structure of the formations. For the reservoir engineer, permeability is generally considered a fundamental reservoir property, the determination of which is at least equal in importance with the determination of porosity, fluid saturations, and formation pressure. When obtainable, cores of the formation provide important data concerning permeability. However, cores are difficult and expensive to obtain, and core analysis is time consuming and provides information about very small sample volumes. In addition, cores, when brought to the surface, may not adequately represent downhole conditions. Thus, in situ determinations of permeability that can quickly provide determinations of permeabilities over large portions of the formation are highly desirable.
Suggestions regarding in situ determination of permeability via the injection or withdrawal of fluid into or from the formation and the measurement of pressures resulting therefrom date back at least to U.S. Pat. No. 2,747,401 to Doll (1956). The primary technique presently used for in situ determination of permeability is the “drawdown” method where a probe of a formation testing tool is placed against the borehole wall, and the pressure inside the tool is brought below the pressure of the formation, thereby inducing fluids to flow into the formation testing tool. By measuring pressures and/or fluid flow rates at and/or away from the probe, and processing those measurements, determinations regarding permeability are obtained. Currently, such determinations are being made via the MDT (a trademark of Schlumberger) tool or Modulation Formation Dynamics Tester, which is a commercially successful tool of Schlumberger, the assignee hereof. However, one drawback to the drawdown method is that it is time consuming and therefore the number of locations at which sampling is accomplished is necessarily quite limited.
Starting in the 1960's it was proposed to use nuclear magnetic resonance (NMR) measurements to measure formation permeability. In particular, it is well known that the strength of a NMR signal is directly proportional to the number of resonated spins present in a probed volume. Because hydrogen is the nucleus of choice in most borehole measurements, and because NMR tools can be tuned in frequency to resonate a particular nuclear species, the signal amplitude of a tuned tool can be arranged to measure the number of hydrogen atoms in the formation. The number of hydrogen atoms in the formation in turn is related to fluid filled porosity. In addition to being sensitive to hydrogen density, NMR tools are sensitive to the environment of the hydrogen being probed. For example, hydrogen in a bound or “irreducible” fluid typically has a spin-lattice relaxation time (T1) in the milliseconds to tens of milliseconds, while free or producible fluid has a T1 in the range of tens to hundreds of milliseconds. Thus, in addition to correlating well to porosity, the measurements resulting from the NMR sequences applied to the formation provide information which may be correlated with the “free fluid index”, permeability, and residual oil saturation. The concept of “free fluid index” is largely based on work by Seevers, “A Nuclear Magnetic Method for Determining the Permeability of Sandstones”, 7th SPWLA Logging Symp. (1966, Paper L), and Timur, “Pulsed Nuclear Magnetic Resonance Studies of Porosity, Movable Fluid, and Permeability of Sandstones”, Journal of Petroleum Technology, (June 1969, pp. 775–786). Currently, NMR measurements in the borehole are being made via the CMR (a trademark of Schlumberger) or Combinable Magnetic Resonance tool, and the MRX (a trademark of Schlumberger) or Magnetic Resonance expert tool which features a gradient magnetic field and multiple frequencies of operation; both of which are commercially successful tools of Schlumberger, the assignee hereof. Details of NMR borehole tools may be seen with reference to U.S. Pat. No. 4,933,638 to Kenyon et al., U.S. Pat. No. 5,023,551 to Kleinberg et al., and U.S. Pat. No. 5,486,761 to Sezginer, all of which are hereby incorporated by reference herein in their entireties.
NMR tools function on the principle that the nuclei of elements such as hydrogen have an angular momentum (“spin”) and a magnetic moment. The nuclear spins will align themselves along an externally applied static magnetic field which may be applied by the NMR tool. The equilibrium situation can be disturbed by a pulse of an oscillating magnetic field provided by the NMR tool which tips the spins away from the static field direction. After tipping, two things occur simultaneously. First, the spins precess around the static field at a particular frequency (i.e., the Larmor frequency), given by ωo=γBo where Bo is the strength of the static field and γ is the gyromagnetic ratio, a nuclear constant. Second, the spins return to the equilibrium direction according to a decay time known as the “spin-lattice relaxation time” or T1. T1 is controlled totally by the molecular environment and is typically ten to one thousand milliseconds in rocks. Each spin can be thought of as moving back toward equilibrium in a very tight pitch spiral during the T1 decay.
Also associated with the spin of molecular nuclei is a second relaxation time known as the “spin—spin relaxation time” or T2. At the end of a ninety degree tipping pulse, all the spins are pointed in a common direction perpendicular to the static field, and they all precess at the Larmor frequency. However, because of small inhomogeneities in the static field due to imperfect instrumentation or microscopic material heterogeneities, each nuclear spin precesses at a slightly different rate. Hence, after a time long compared to the precession period, but shorter than T1, the spins will no longer be precessing in unison. When this dephasing is due to static field inhomogeneity of the apparatus, the dephasing is called T2*. When it is due to properties of the material, the dephasing time is called T2. For rocks, T2 is generally approximately one-half of T1.
While many different methods for measuring T1 have been developed, a relatively standard method known as the CPMG (Carr-Purcell-Meiboom-Gill) sequence has been used to measure T2. The CPMG sequence is a well-known sequence of pulses which cancel out the effect of the apparatus-induced inhomogeneities and permit a determination of dephasing due to material properties; i.e., a measurement of T2. Modifications to the CPMG sequence such as set forth in previously incorporated U.S. Pat. No. 5,023,551 to Kleinberg et al. have been utilized to improve thereupon.
As is well known in the art, after applying the CPMG sequences, NMR tools measure a voltage or magnetization over time which is designated M(t). As will be discussed hereinafter, M(t) is a function of porosity φ, the observed T2 decay T2o, and a probability density function g0 of the distribution of T2 relaxation in the rock pores contributing to the signal. Thus, from M(t), the porosity φ can be calculated. Also, for water saturated pores, a correlation has been developed which permits a determination of permeability k according to k=C1φ2T2lm2, where C1 is a constant, and T2lm is the T2 log mean.
While the permeability determination utilizing the correlation yields reasonable results for water saturated pores, it has been more difficult to measure permeability in rocks where there is water and oil. Where there is water and oil, if the water wets the pore walls, then the oil in the pore relaxes as if there is no pore wall. As a result, the T2lm appears to be larger than it should otherwise be, and the permeability determination is skewed.
One manner of correcting for the problem of measuring permeability in the presence of water and oil is to generate an indication of the T2 signal, and to partition the signal via a cutoff time (e.g., 33 milliseconds) with the T2 signal prior to the cutoff time being considered related to the bound water. The bound water is the irreducible water saturation (swi) which is related to permeability according to the Timur correlation k=cφb/swid, where c is a constant usually taken as 0.136, b is a constant usually taken as 4.4, and d is a constant usually taken as 2. See SPE 30978 (1968).
The Timur correlation, while sometimes providing reasonable results, is considered error prone. Indeed, historically, the permeability predictors based on NMR relaxation have been hindered by a host of uncertainties, including (i) unknown surface relaxivity (i.e., rate at which magnetization decays at a pore wall) parameter, (ii) failure of correlations developed for fully saturated rocks when applied to hydrocarbon zones, and (iii) inadequate pore network physics in relating T2 distribution to permeability.